Look-ahead delta sigma modulators with quantizer input approximations

ABSTRACT

A signal processing system includes a look-ahead delta sigma modulator having an approximation generator to approximate quantizer input signals. A look-ahead delta-sigma modulator can be implemented as a noise shaping filter and a quantizer. The quantizer can be implemented as a function generator. State variables of the noise shaping filter provide the input data from which the function generator determines a quantizer output signal. Latter state variables are more dominant in determining the quantizer output signal. Accordingly, earlier state variables can be approximated to a greater degree than earlier state variables. The approximations can result in slightly lower output signal accuracy but can significantly decrease implementation cost. Additionally, latter state variables can completely dominate (i.e., be deterministic) the quantizer output signal. This situation can result in a further, slight increase in the non-linearity of one or more quantization region boundaries.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit under 35 U.S.C. § 119(e) of (i) U.S.Provisional Application No. 60/537,285, filed Jan. 16, 2004 and entitled“Look-Ahead Delta-sigma Modulators”, (ii) U.S. Provisional ApplicationNo. 60/539,132, filed Jan. 26, 2004 and entitled “Signal ProcessingSystems with Look-Ahead Delta-Sigma Modulators”, and (iii) U.S.Provisional Application No. 60/588,951, filed Jul. 19, 2004 and entitled“Signal Processing Systems with Look-Ahead Delta-Sigma Modulators”.Provisional applications (i) through (iii) include example systems andmethods and are incorporated by reference in their entireties.

This application claims the benefit under 35 U.S.C. § 120, and is acontinuation-in-part, of commonly assigned U.S. patent application No.______, attorney docket number 1532-CA, filed on Jan. 13, 2005, entitled“Jointly Non-linear Delta Sigma Modulators,” inventor John L. Melanson.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates in general to the field of informationprocessing, and more specifically to a system and method forapproximating input signals to quantizers of look-ahead delta-sigmamodulators.

2. Description of the Related Art

Many signal processing systems include delta sigma modulators toquantize an input signal into one or more bits. Delta sigma modulatorstrade-off increased noise in the form of quantization error in exchangefor high sample rates and noise shaping. “Delta-sigma modulators” arealso commonly referred to using other interchangeable terms such as“sigma-delta modulators”, “delta-sigma converters”, “sigma deltaconverters”, and “noise shapers”.

FIG. 1 depicts a conventional delta sigma modulator 100 that includes amonotonic quantizer 102 for quantizing a digital input signal x(n),where “x(n)” represents the n^(th) input signal sample. The delta sigmamodulator 100 also includes an exemplary fourth (4^(th)) order noiseshaping loop filter 104 that pushes noise out of the signal band ofinterest. The output data of each stage 106(1), 106(2), 106(3), and106(4) of the filter 104 is represented by respective state variablesSV1, SV2, SV3, and SV4 of filter 104. The state variables are updatedonce during each operational period T. The quantizer input signal s(n)is determined from a linear combination of the state variables inaccordance with the topology of filter 104. The complete quantizer inputsignal s(n) is determined from the state variables modified byfeed-forward gains d1 through d4 and input signal x(n) modified byfeedback coefficient c0 and feed-forward gain d0. For audio signals, thesignal band of interest is approximately 0 Hz to 20 kHz. The fourfeedback coefficients c0, c1, c2, and c3 and/or the feed-forwardcoefficients set the poles of both the noise transfer function (NTF) andthe signal transfer function (STF) of filter 104. In general, there aretwo common filter topologies, feed-forward and feedback. In the feedbackcase, the feed-forward coefficients are all zero, except for the lastcoefficient. In the feed-forward case, all of the feedback coefficientsare 0, except for c0, which is usually defined as 1, without any loss ofgenerality. The NTF of filter 104 has four (4) zeros at DC (0 Hz). Localresonators are often added, with feedback around pairs of integrators,in order to move some of the zeroes to frequencies higher in the signalpassband. Typical high performance delta sigma modulators include fourth(4^(th)) order and higher loop filters although filter 104 can be anyorder. The NTF often distributes zeros across the signal band ofinterest to improve the noise performance of the delta sigma modulator100.

The topology of each stage is a matter of design choice. Stages 106(i)are each represented by the z-domain transfer function of z⁻¹/(1−z⁻¹).Group 108 is functionally identical to group 110. Stage 106(1) can berepresented by a leading edge triggered delay 112 and feedback 114.

FIG. 2 depicts the quantizer 102 modeled as a gain, g, multiplying thequantizer input signal s(n) plus additive white noise n. The quantizeroutput noise is then modeled as n/(1+z⁻¹*g*H(z)). However, the quantizeroutput noise model often breaks down because the gain g is actuallydependent upon the level (magnitude) of the input signal x(n).Additionally, the additive noise is correlated to the input signal. Forlow level input signals x(n), a tendency exists for the feedback signalinto the quantizer 102 to be low, effectively making the gain high orbreaking down the quantizer output noise model altogether. Becauseone-bit quantizers have no well-defined gain, a high gain for low levelquantizer input signals is particularly bad because it can decrease thesignal-to-noise ratio (SNR) of the delta sigma modulator 100. Oftenwhite noise, or dither, is added to the input of the quantizer in orderto aid this situation; however that noise decreases the dynamic rangeand maximum signal input of the system.

Referring to FIGS. 1, 2, and 3, the quantizer 102 quantizes an inputsignal x(n) monotonically by making a decision to select the closestfeedback value to approximate the input signal. In a one-bit delta sigmamodulator, the quantizer has only two legal outputs, referred to as −1and +1. Therefore, in a one-bit embodiment, quantizer 102 quantizes allpositive input signals as a +1 and quantizes all negative input signalsas −1. The quantization level changeover threshold 304 is set at DC,i.e. 0 Hz, and may be quantized as +1 or −1.

FIG. 3 graphically depicts a monotonic, two-level quantization transferfunction 300, which represents the possible selections of each quantizeroutput signal y(n) from each quantizer input signal s(n). The diagonalline 302 depicts a monotonic unity gain function and represents thelowest noise quantization transfer function. “Monotonic” is defined by afunction that, as signal levels increase, consists of either increasingquantizer output state transitions (“transitions”) or decreasingtransitions, but not both increasing and decreasing transitions. Tomathematically define “monotonically increasing” in terms ofquantization, if the transfer function of the quantizer 102 is denotedas Q(s), then Q(s1)≧Q(s2), for all s1>s2, where “s1” and “s2” representquantizer input signals. Mathematically defining “monotonicallydecreasing” in terms of quantization, if the transfer function of thequantizer 102 is denoted as Q(s), then Q(s1)≧Q(s2), for all s1<s2. Thus,in general, a monotonic quantization transfer function must adhere toEquation 1:Q(s 1)>Q(s 2), for all |s 1|>|s 2|.   [Equation 1]

In many cases, dithering technology intentionally adds noise to thequantizer input signal s(n) to dither the output decision of quantizer102. Adding dithering noise can help reduce the production of tones inthe output signal y(n) at the cost of adding some additional noise tothe delta sigma modulator loop because the quantization noise isgenerally increased. However, adding dithering noise to the quantizerdoes not convert a monotonic quantization transfer function into anon-monotonic quantization transfer function. Adding dithering noisemerely changes the probability of some quantizer decisions. Analternative perspective regarding dither is to simply add a signal priorto quantization, which has no effect on the quantization transferfunction.

Magrath and Sandier in A Sigma-Delta Modulator Topology with HighLinearity, 1997 IEEE International Symposium on Circuits and Systems,Jun. 9-12, 1987 Hong Kong, (referred to as “Magrath and Sandler”)describes a sigma-delta modulator function that achieves high linearityby modifying the transfer function of the quantizer loop to includebit-flipping for small signal inputs to the quantizer. Magrath andSandler discusses the compromise of linearity of the sigma-deltamodulation process by the occurrence of idle tones, which are stronglyrelated to repeating patterns at the modulator output and associatedlimit cycles in the system state-space. Magrath and Sandler indicatesthat injection of a dither source before the quantizer is a commonapproach to linearise the modulator. Magrath and Sandler discusses atechnique to emulate dither by approximately mapping the dither onto anequivalent bit-flipping operation.

FIG. 4 graphically depicts the single non-monotonic region quantizationtransfer function 400 that emulates dither as described by Magrath andSandler. Quantizer function 400 is necessarily centered around s(n)=0,as described by Magrath and Sandler, to emulate conventional dither.According to Magrath and Sandler, if the absolute value of the input(“|s(n)|” in FIG. 1) to the quantizer is less than B, a system constant,then the quantizer state is inverted as depicted by quantizer function400.

Input signals s(n) to the quantizer 102 can be represented byprobability density functions (PDFs). FIG. 5A depicts PDFs of eachquantizer input signal s(n) during operation at small and large inputsignal levels. PDF 502 represents small signal levels for each signals(n). The narrow PDF 502 can indicate high delta sigma modulator loopgain g. As the magnitude of signal levels for signal s(n) increase, thePDF of each signal s(n) changes from the narrow PDF 502 to the wider PDF504.

FIG. 5B depicts a near ideal PDF 500 for each quantizer input signals(n) because all signals are clustered around the quantization levels +1and −1. Accordingly, the quantization noise n (error) is very small.

FIG. 6 graphically depicts a convex region 602 and a nonconvex region604. A set in Euclidean space is a convex set if the set contains allthe line segments connecting any pair of points in the set. If the setdoes not contain all the line segments connecting any pair of datapoints in the set, then the set is nonconvex (all referred to as“concave”). The convex region 602 includes all sets of data pointswithin the boundaries of convex region 602. As depicted by the exampleline segments AB and CD, all line segments in convex region 602connecting any pair of data points are completely contained withinconvex region 602

Region 604 represents a nonconvex region because there exists at leastone line segment AB connecting a pair points {A,B} that is notcompletely contained within region 603. Thus, by definition, region 604is a nonconvex region.

FIG. 7A depicts the interrelationship of two state variables SVx and SVywith respect to the output y(n) of a monotonic quantizer 102 (FIG. 1).State variables SVx and SVy represent any respective state variable offilter 104. Line 702 represents the boundary between the +1 quantizationregion and the −1 quantization region for a quantization output level.The boundary 702 of the quantization regions +1 and −1 is characterizedby a linear interrelationship between state variables SVx and SVy. Thequantization regions +1 and −1 are also defined by convex boundaries. Inthe case of a feedback topology for the loop filter, the quantizer isresponsive to only one state variable, that being the last (or highestorder) one. In the case of a feed-forward filter topology, therelationship illustrated in FIG. 7A is active. In general, the regionswill have dimensionality of the order of the filter, e.g., a fourthorder filter would have a 4-space diagram. The 2 dimensional diagramsare meant to be representative of a 2-dimensional slice of an actualn-dimensional region functions being depicted.

FIG. 7B depicts the interrelationship between two state variables SVxand SVy with respect to the output y(n) of a bit-flipping quantizer 102.The boundaries between quantization regions A, B, C, and D are linear.The non-monotonic, bit-flipping quantizer 102 has four, convexquantization regions that alternate twice between +1 and −1. The fourquantization regions are also defined by a linear relationship for anypair of state variables SVx and SVy. Again, in a higher order system,the actual regions depicted are n-dimensional.

Conventional research in look-ahead modulators primarily involves twothreads. The first are the works of Hiroshi Kato, “Trellis Noise-ShapingConverters and 1-bit Digital Audio,” AES 112^(th) Convention, May 10-132002 Munich, and Hiroshi Kato, Japanese Patent JP, 2003-124812 A, andfurther refinements described in Harpe, P., Reefman D., Janssen E.,“Efficient Trellis-type Sigma Delta Modulator,” AES 114^(th) Convention,Mar. 22-25 2003 Amsterdam (referred to herein as “Harpe”); James A. S.Angus, “Tree Based Look-ahead Sigma Delta Modulators,” AES 114^(th)Convention, Mar. 22-25 2003 Amsterdam; James A. S. Angus, “EfficientAlgorithms for Look-Ahead Sigma-Delta Modulators,” AES 155^(th)Convention, Oct. 10-13 2003 New York; Janssen E., Reefman D., “Advancesin Trellis based SDM structures,” AES 115^(th) Convention, Oct. 10-132003 New York. This research targets solving the problems of 1-bitencoding of audio data for storage without using the steep anti-aliasfilters associated with pulse code modulation “PCM.” The advent of superaudio compact disc “SACD” audio storage, with its moderate oversamplingratios (32 or 64), motivated this work.

FIG. 8A depicts a prior art signal processing system 800 having alook-ahead delta-sigma modulator 802. The signal source 802 provides aninput signal to pre-processing components 804. Preprocessing components804 include an analog-to-digital converter (“ADC”) and oversamplingcomponents to generate a k-bit, digital input signal x(n). For audioapplications, x(n) generally represents a signal sampled at 44.1 kHztimes an oversampling ratio, such as 64:1. Look-ahead modulator 806includes loop filter 808 to shape quantization noise so that most of thequantization noise is moved out of the signal band of interest, e.g.approximately 0-20 kHz for audio applications. Look-ahead modulator 806also includes quantizer 810 to choose a best output candidate vector810, quantize the output of loop filter 808 with quantizer 812 inaccordance with the chosen output candidate vector 810, provide outputsignal y(n), and update the state variables of loop filter 808 using theactual output signal y(n). Each output signal y(n) (also referred toherein as an “output value”) generally has one of two values selectedfrom the set {+Δ/2, −Δ/2} with “Δ” representing the full swing of y(n).(For convenience, Δ/2 will be represented as +1, and −Δ/2 will berepresented as −1.). The output signal y(n) can be further processedand, for example, used to drive an audio sound system or can be recordeddirectly onto a storage medium. The Background section of commonlyassigned U.S. patent application Ser. No. 10/995,731, filed Nov. 22,2004, entitled “Look-ahead Delta Sigma Modulator with Quantization UsingNatural and Pattern Loop Filter Responses”, inventor John L. Melanson(referred to herein as the “Melanson I”) contains an exemplarydescription of conventional look-ahead delta sigma modulator operations.

The second primary thread of look-ahead modulator research involvespulse width modulation (“PWM”) amplifiers based on delta-sigmamodulators combined with digital PWM modulation stages. The principalresearchers have been Peter Craven and John L. Melanson. In U.S. Pat.No. 5,784,017 entitled “Analogue and Digital Converters Using Pulse EdgeModulations with Non-Linear Correction,” inventor Peter Craven(“Craven”), which is incorporated herein by reference in its entirety,Craven described the use of look-ahead operations in delta-sigmamodulators. The purpose of Craven was to ensure stability in alternatingedge modulation, an inherently difficult modulation mode to stabilize.In the PWM case, the delta-sigma modulator is operating at a lowoversampling ratio (typically 4-16), and quantization noise is a specialproblem.

FIG. 8B depicts quantizer 806 and noise shaping loop filter 808. Thefilter 808 can be considered as having a noise transfer function (“NTF”)and a separate signal transfer function (“STF”), as described incommonly assigned U.S. patent application Ser. No. 10/900,877, filedJul. 28, 2004, entitled “Signal Processing with Lookahead ModulatorNoise Quantization Minimization”, inventor John L. Melanson and inchapter 4 of Norsworthy et al, “Delta Sigma Data Converters—Theory,Design, and Simulation”. 1997, ISBN 0-7803-1045-4. The noise transferfunction (“NTF”) equals 1/[1+z⁻¹*H₂(z)]. Filter 808 is modeled toindicate the signal transfer function H₁(z), the feedback signaltransfer function H₂(z), and quantization noise 814. The signal transferfunction (“STF”) equals H₁(z)/[1+z⁻¹*H₂(z)]. In some implementations, H1and H2 are identical. In the general case, H1 and H2 differ.

Conventional look-ahead delta sigma modulators require a significantamount of computation and state storage. For a look-ahead depth of 8bits, in the simplest case 256 copies of the delta sigma modulator arerequired. Most research has been directed to simplifying the computationby pruning the search so that only a moderate fraction of the 2^(M)cases are calculated.

SUMMARY OF THE INVENTION

In one embodiment of the present invention, a signal processing systemincludes a look-ahead delta sigma modulator. The look-ahead delta sigmamodulator includes a noise shaping filter to process a signal andgenerate N state variables, wherein N is an integer greater than orequal to two and an approximation generator coupled to the noise shapingfilter to generate approximated state variables determined from at leasta subset of the N state variables. The look-ahead delta sigma modulatoralso includes a quantizer coupled to the approximation generator toquantize quantizer input data determined from the approximated statevariables and determine a quantization output value with an objective ofminimizing quantization error at a current and at least one future timestep.

In another embodiment of the present invention, a method of processing asignal using a look-ahead delta-sigma modulator that includes a noiseshaping filter having N state variables, wherein N is an integer greaterthan or equal to two, includes filtering an input signal to thelook-ahead delta-sigma modulator using the noise shaping filter togenerate the N state variables. The method further includes generatingapproximated state variables determined from at least a subset of the Nstate variables and quantizing the quantizer input data determined fromthe approximated state variables to determine a quantization outputvalue with an objective of minimizing quantization error at a currentand at least one future time step.

In a further embodiment of the present invention, an apparatus includesmeans for filtering an input signal to the look-ahead delta-sigmamodulator to generate N state variables, wherein N is an integer greaterthan or equal to two. The apparatus further includes means forgenerating approximated state variables determined from at least asubset of the N state variables and means for quantizing the quantizerinput data determined from the approximated state variables to determinea quantization output value with an objective of minimizing quantizationerror at a current and at least one future time step.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention may be better understood, and its numerousobjects, features and advantages made apparent to those skilled in theart by referencing the accompanying drawings. The use of the samereference number throughout the several figures designates a like orsimilar element.

FIG. 1 (labeled prior art) depicts an exemplary delta sigma modulatorwith a monotonic quantizer.

FIG. 2 (labeled prior art) depicts an exemplary delta sigma modulatorquantizer model.

FIG. 3 (labeled prior art) depicts an exemplary monotonic, two-levelquantization transfer function.

FIG. 4 (labeled prior art) depicts an exemplary single non-monotonicregion quantization transfer function for dither emulation.

FIG. 5A (labeled prior art) depicts exemplary probability densityfunctions of each quantizer input signal during operation at small andlarge input signal levels.

FIG. 5B (labeled prior art) depicts an exemplary near ideal probabilitydensity function for each delta sigma modulator quantizer input signal.

FIG. 6 (labeled prior art) depicts convex and nonconvex regions.

FIG. 7A (labeled prior art) depicts the interrelationship of two noiseshaping filter state variables with respect to the output of a monotonicquantizer.

FIG. 7B (labeled prior art) depicts the interrelationship of two noiseshaping filter state variables with respect to the output of a ditheringquantizer.

FIG. 8A (labeled prior art) depicts a signal processing system having alook-ahead delta-sigma modulator.

FIG. 8B (labeled prior art) depicts a quantizer and noise shapingfilter.

FIG. 9A depicts an exemplary jointly non-linear delta sigma modulator.

FIG. 9B depicts an exemplary loop filter.

FIG. 10 depicts an exemplary lookahead, jointly non-linear delta sigmamodulator that includes a function generator for quantization.

FIG. 11 depicts an exemplary function generator of the delta sigmamodulator of FIG. 10.

FIG. 12 depicts an add/compare/select network.

FIG. 13 depicts an example loop-up table embodiment of quantizerfunction generator.

FIGS. 14A, 14B, 14C, 14D, 14E, and 14F depict exemplary embodiments ofquantization region boundaries characterized by non-linearinterrelationships between at least two delta sigma modulator filterstate variables.

FIG. 14G depicts a functional implementation to generate the jointlynon-linear function depicted in FIG. 14A.

FIG. 15 depicts an exemplary probability density function of eachquantizer input signal.

FIG. 16 depicts an exemplary signal processing system that includes alook-ahead modulator, an output device and process, and an outputmedium.

FIG. 17 exemplary depicts post-processing operations in an embodiment ofthe signal processing system of FIG. 16.

DETAILED DESCRIPTION

A signal processing system includes a look-ahead delta sigma modulatorhaving an approximation generator to approximate quantizer inputsignals. A look-ahead delta-sigma modulator can be implemented as anoise shaping filter and a quantizer. The quantizer can be implementedas a function generator. State variables of the noise shaping filterprovide the input data from which the function generator determines aquantizer output signal. Latter state variables are more dominant indetermining the quantizer output signal. Accordingly, earlier statevariables can be approximated to a greater degree than earlier statevariables. The approximations can result in slightly lower output signalaccuracy but can significantly decrease implementation cost.Additionally, latter state variables can completely dominate (i.e., bedeterministic) the quantizer output signal. This situation can result ina further, slight increase in the non-linearity of one or morequantization region boundaries.

In one embodiment, the look-ahead delta sigma modulator is implementedas a jointly non-linear delta sigma modulator. In one embodiment, thejointly non-linear delta sigma modulator includes a non-linearquantization transfer function, and one or more boundaries betweenquantization regions of the output of the delta sigma modulator arecharacterized, at least in part, by a non-linear interrelationship ofmultiple noise-shaping filter state variables. Thus, in at least oneembodiment, “jointly non-linear” refers to a nonlinear quantizationtransfer function that quantizes an input signal in accordance withdiscrete one-bit or multi-bit levels together with non-linearquantization region boundaries characterized by a non-linearinterrelationship between multiple noise-shaping filter state variables.

The non-linear interrelationships between N filter state variables canrepresent an N dimensional set of relationships that characterize theboundaries of the quantization regions of the quantizer output. Thequantization regions can be convex or nonconvex. Furthermore, thequantization regions can also include one or more monotonic and/ornon-monotonic regions for one-bit and multi-bit delta-sigma modulators.In one embodiment, the jointly non-linear delta sigma modulator includesone or more quantization levels with quantization region boundariescharacterized by a non-linear interrelationship between at least twopairs of delta sigma modulator, noise shaping filter state variables.Embodiments of the jointly non-linear nature of the delta sigmamodulator improve overall delta sigma modulator performance byincreasing computational performance and, with regard to non-monotonicembodiments, making a slightly worse short-term quantization decision inexchange for making better long-term decisions. goal

In general, look-ahead delta sigma modulators determine a quantizationoutput value from output candidate vectors and input vectors. Theobjective of the quantizer of a look-ahead delta-sigma modulator is tominimize quantization error at a current and at least one future timestep. In other words, for a given time index of t, the look-aheaddelta-sigma modulator selects a quantization output value that attemptsto minimize quantization error for the current time t and for a futuretime, such as t+1. The look-ahead depth refers to the dimension of eachoutput candidate vector Yi used to determine output signal y(n). From afunctional viewpoint, for time t, each output candidate vector Yi,iε{0,1,2, . . . , M-1}, is subtracted from an input vector Xt to obtainrespective difference vectors Di, iε{0,1,2, . . . , M-1}, andDi=[Xt−Yi]. The leading bit of the best matching output candidate vectoris chosen as the quantization output y(n). Melanson I, II, and IIIdescribe various exemplary systems and methods for determiningquantization output y(n).

FIG. 9A depicts a jointly non-linear delta sigma modulator 900 thatquantizes each quantizer input signal s(n) with a quantizer 902. Thequantizer input signal s(n) includes state variables SV₁, . . . ,SV_(K), where K is less than or equal to the total number filter 904state variables. One or more embodiments of delta sigma modulator 900are jointly non-linear delta sigma modulators that can be designed toemulate a prototypical look-ahead delta sigma modulator. For purposes ofthe present invention, delta sigma modulators that emulate look-aheaddelta sigma modulators will be considered as delta sigma modulators.Filter 904 processes each delta sigma modulator input signal x(n) minusa delayed quantizer output signal y(n), i.e. x(n)−y(n-1), to generatethe quantizer input signal s(n). Filter 904 can be any noise-shapingfilter, such as filter 104. Quantizer 902 quantizes quantizer inputsignal s(n) in accordance with a non-linear quantization transferfunction Q(s(n)). U.S. patent applications (i) Melanson I, (ii) Ser. No.10/875,920, filed Jun. 24, 2004, entitled “Signal Processing with aLook-Ahead Modulator Having Time Weighted Error Values”, and inventorJohn L. Melanson (referred to herein as “Melanson II”), and (iii) Ser.No. 10/900,877, filed Jul. 29, 2004, entitled “Signal Processing withLook-Ahead Modulator Noise Quantization Minimization”, and inventor JohnL. Melanson (referred to herein as “Melanson III”), describe variousexemplary look-ahead delta sigma modulators. Melanson I, Melanson II,and Melanson III are hereby incorporated by reference in theirentireties. Filter 904 can be implemented using any topology, such asfeed-forward or feedback topologies. Example loop filters are describedin “Delta-Sigma Data Converters—Theory, Design, and Simulation”, editedby Norsworthy, et al., 1997, IEEE Press, and ISBN 0-7803-1045-4.

In one embodiment, filter 904 includes multiple stages and N statevariables, and N is an integer ≧3. A subset of the N state variables offilter 904 are represented by state variables SV_(A), . . . , SV_(K),where A and K are integers, 2≦A≦K≦N. In one embodiment, at least two ofthe state variables from the set {SV_(A), . . . , SV_(K)} have anonlinear interrelationship that characterize, at least in part, one ormore boundaries between two or more quantization regions of thequantizer output. The state variables SV_(A), . . . , SV_(K) generatedby filter 904 represent output data of filter 904. The quantizer outputfunction Q(s(n)) is a function of at least a subset of state variablesSV_(A), . . . , SV_(K), (Q(s(n))=f(SV_(A), . . . , SV_(K)), and Q(s(n))can be linear or non-linear. In one embodiment, the quantizer functionis a function of the J+1 most significant state variables, i.e.Q(s(n)=f(SV_(N-J), . . . , SV_(N-1), SV_(N)), 1≦J≦N-1, N represents thetotal number of filter 904 state variables, and SV_(N) is the statevariable associated with the last integrator of filter 904, e.g. forN=4, integrator 106(4) of FIG. 1. “J” is an integer whose value isselected to identify the earliest state variable to be approximatedbased on the order of filter 904 stages. State variables from stagesearlier than N-J are approximated to zero (0).

The latter stage integrators of look-ahead delta sigma modulatorsgenerally have a predominant effect on the quantization decision ofquantizer 902. Thus, as described in more detail below, in oneembodiment delta sigma modulator 900 can employ approximation techniquesthat place more emphasis on the latter stage integrators with anacceptable amount of error. In other embodiments, any subset {SV_(A), .. . , SV_(K)} of the N state variables of filter 904 can be approximatedby approximation generator 906 to generate SV_(A)′, . . . , SV_(K)′.

Referring to FIGS. 9A and 9B, loop filter 908 represents one embodimentof loop filter 904. The topology of noise shaping filter 908 istypically arranged a cascade of integrators, the last integrator 910 hasthe largest effect on the selection of quantization output y(n), whichis true even with multiple feedback loops as indicated by thedenominators of each sub-system transfer function 912(1), . . . ,912(N-1), and 912(N). Since the latter integrators have a predominanteffect on the selection of quantization output y(n), in some embodimentsof delta sigma modulator 900 a subset of the state variables areapproximated with successive increased approximations of earlierintegrators. In some embodiments, only a subset of the state variablesof filter 908 are considered in determining the quantization outputy(n). Thus, selected filter 908 state variables SV_(N), SV_(N-1), . . ., SV_(N-J) form the inputs to optional preprocessor I 905. PreprocessorI 905 can preprocess the state variables by, for example, applyingrespective gains to one or more of the state variables or one or morecombinations of the state variables. In another embodiment, thepreprocessor I 905 can combine one or more state variables.

If preprocessor I 905 is used, the output of preprocessor I 905 providesthe inputs to approximation generator 906. If preprocessor I 1005 is notused, the state variables are applied directly to approximationgenerator 1006. Approximation generator 906 provides approximated statevariables SV_(N)′, SV_(N-1)′, . . . , SV_(N-J)′ as input data to thequantizer 902 if the preprocessor II 907 is not used. Beforeapproximating any state variable, each state variable is typicallyrepresented by between ten (10) and thirty (30) bits. In one embodiment,the state variable having a predominant influence on the value of theoutput signal y(n) are each approximated to varying degrees dependingupon the influence of the particular state variable. Greaterapproximation reduces implementation costs such as memory requirementsand reduces computational operations. However, greater approximationresults in less accuracy, but the trade-off in implementation costs canmore than offset the loss of accuracy. The exact trade-off is a matterof design choice and is achieved at least in one embodiment throughtrial and error. For example, in one embodiment, K=N and A=N−J, for N=5and J=2 and each state variable is represented by 10 bits, statevariable SV_(N)′ is represented by w=6 bits (i.e. an approximation offour (4) bits), SV_(N-1)′ is represented by v=5 bits, SV_(N-2)′ isrepresented by u=4 bits, and state variables SV_(N-J-1) through SV₁ areapproximated to zero (i.e. ignored). Because of the predominance of thelatter state variables in determining the quantization output y(n), theapproximations result in a slightly lower accuracy of quantizationoutput y(n) but disproportionately decrease implementation costs.Generally, with a feed-forward filter, combinations of state variablesare used by quantizer 902. The preprocessor II 907 is optionally used tofurther preprocess the approximated state variables by, for example,applying respective gains to one or more of the approximated statevariables or to one or more combinations of the approximated statevariables. Using gained combinations of elements determined from statevariables makes the search space for a quantization output value smaller(e.g. the size of look-up table 1300 of FIG. 13 can be smaller byreducing the number of rows), particularly in the case where aninteresting part of the quantization function is oblong, not circular.Generally, preprocessors I and II will perform distinct operations.Additionally, the input sample x(n) can also be used as an input byquantizer 902 to determine the output y(n). By adding r delays to theinput of filter 1004, future input samples x(n+1), x(n+2), . . . x(n+r)can also be used as inputs to quantizer 902 to determine the outputy(n), where r is an integer. In other embodiments, one or moreoperations of preprocessor I 905 and/or preprocessor II 907 areperformed by filter 904.

Approximation generator 906 can be used with any look-ahead (includingemulated look-ahead) delta-sigma modulators including monotonic andnon-monotonic look-ahead delta-sigma modulators. Approximation generator906 can be logically considered as an independent, intermediarycomponent between filter 904 and quantizer 902 or as a functionalcomponent of quantizer 902.

FIG. 10 depicts a lookahead, jointly non-linear delta sigma modulator1000 that includes an Nth order noise shaping filter 1004, such asfilter 104 and a quantizer 1001 implemented by a jointly non-linearfunction generator 1002. The look-ahead delta sigma modulator 1000represents one embodiment of delta sigma modulator 900. The output dataof each integrator of filter 104 represents the state variables SV_(N),SV_(N-1), . . . , SV₁. The value of each state variable for each inputx(n) is a function of the input x(n) and the topology of filter 1004including the coefficients, c₀, c₁, . . . , c_(N-1), C_(N) and feedbackdata y(n−1).

When look-ahead delta sigma modulators are implemented, a searchdetermines the best output candidate vector. If the output candidatevector is M elements long (look-ahead depth of M), a 1 bit system, andno search pruning is performed, the search has 2{circumflex over ( )}Moutput candidate vectors to process. Even with pruning, andsimplifications, this search is still computationally expensive.

Melanson I describes an exemplary system and method for determining thequantizer output data y(n) for each time t using forced pattern responsevectors (SPAT_(k)) and a natural input response vector (SNAT). SPAT_(i)represents the response of a noise shaping filter, such as filter 1004,to 0 input and feedback from the k^(th) output candidate vector. Asdescribed in Melanson I, the SPAT response vectors can be calculatedonce and stored. SNAT_(t) represents the response of the filter to theinput vector X_(t) at time t and feedback forced to 0, X_(t)={x(n),x(n+1), . . . , x(n+M)}_(t).

In addition to describing an exemplary system and method for reducingthe number of pattern response vectors used to determine thequantization output y(n), Melanson I also describes an exemplary systemof efficiently determining the best matching forced pattern responsevector SPAT_(k min) and selecting the value of quantization output y(n)as the leading bit of the best matching pattern response vector. Theselected quantization output y(n) is fed back through delay 1008. Theactual filter 1004 topology and implementation (e.g. software, hardware,or a combination of hardware and software plus coefficients) is a matterof design choice.

Once the filter topology is established and the forced pattern responsevectors SPATs are determined, the quantizer can be implemented as afunction generator 1002 using the state variables of filter 1004 asinput data. Thus, quantizer output y(n) is determined by a quantizationfunction of selected filter state variables, i.e. y(n)=Q(selected filterstate variables). Thus, the jointly non-linear function generator can beviewed as a computational short-cut to implementing the effect thatwould have been achieved with look-ahead delta sigma modulators withstandard full computations.

In one embodiment, assuming the topology of noise shaping filter 1004can be arranged into a cascade of integrators, the last integrator 1010has the largest effect on the selection of quantization output y(n),which is true even with multiple feedback loops as indicated by thedenominators of each sub-system transfer function 1012(1), . . . ,1012(N-1), and 1012(N). Since the latter integrators have a predominanteffect on the selection of quantization output y(n), in some embodimentsof delta sigma modulator 1000 a subset of the state variables areapproximated with successive increased approximations of earlierintegrators. In some embodiments, only a subset of the state variablesof filter 1004 are considered in determining the quantization outputy(n). Thus, selected filter 1004 state variables SV_(N), SV_(N-1), . . ., SV_(N-J) form the inputs to optional preprocessor I 1005. PreprocessorI 1005 can preprocess the state variables by, for example, applyingrespective gains to one or more of the state variables or one or morecombinations of the state variables. In another embodiment, thepreprocessor I 1005 can combine one or more state variables.

If preprocessor I 1005 is used, the output of preprocessor I 1005provides the inputs to approximation generator 1006. If preprocessor I1005 is not used, the state variables are applied directly toapproximation generator 1006. Approximation generator 1006 providesapproximated state variables SV_(N)′, SV_(N-1)′, . . . , SV_(N-J)′ asinput data to the jointly non-linear function generator 1002 if thepreprocessor II 1007 is not used. Before any approximating any statevariable, each state variable is typically represented by between ten(10) and thirty (30) bits. In one embodiment, the state variable havinga predominant influence on the value of the output signal y(n) are eachapproximated to varying degrees depending upon the influence of theparticular state variable. Greater approximation results in lessaccuracy, but the trade-off in implementation costs can more than offsetthe loss of accuracy. The exact trade-off is a matter of design choice.For example, in one embodiment for N=5 and J=2 and each state variableis represented by 10 bits, state variable SV_(N)′ is represented by w=6bits (i.e. an approximation of four (4) bits), SV_(N-1)′ is representedby v=5 bits, SV_(N-2)′ is represented by u=4 bits, and state variablesSV_(N-J-1) through SV₁ are approximated to zero (i.e. ignored). Becauseof the predominance of the latter state variables in determining thequantization output y(n), the approximations result in a slightly loweraccuracy of quantization output y(n) but disproportionately decreaseimplementation costs. The preprocessor II 1007 is optionally used tofurther preprocess the state variables by, for example, applyingrespective gains to one or more of the approximated state variables orto one or more combinations of the approximated state variables.Generally, preprocessors I and II will perform distinct functions.Additionally, the input sample x(n) can also be used as an input byquantizer 1001 to determine the output y(n). By adding r delays to theinput of filter 1004, future input samples x(n+1), x(n+2), . . . x(n+r)can also be used as inputs to quantizer 1001 to determine the outputy(n), where r is an integer. In other embodiments, one or more functionsof preprocessor I 1005 and/or preprocessor II 1007 are performed byfilter 1004.

Depiction of approximation generator 1006 as a functional component ofquantizer 1001 is generally arbitrary and a matter of design choice.Approximation generator 1006 can be logically considered as anindependent, intermediary component between filter 1004 and quantizer1001.

FIG. 11 depicts an exemplary function generator 1100 representing oneembodiment of the function generator 1002. The function generator 1100determines a quantization output y(n) from state variables SV_(N)′,SV_(N-1)′, . . ., SV_(N-J)′ using the computation reduction scheme 1102and quantizer-selector 1104. The function generator can be implementedusing software instructions stored in a memory, such as a read-onlymemory (ROM) and/or using hardware such as an application specificintegrated circuit (ASIC) or field programmable gate array (FPGA). Theinputs to the function generator 1100 are the state variables SV_(N)′,SV_(N-1)′, . . . , SV_(N-J)′. As described below, the state variablesSV_(N)′, SV_(N-1)′, . . . , SV_(N-J)′ are determined from the statevariables SV_(N), SV_(N-1), . . . , SV_(N-J) of filter 1004. Melanson Idescribes the full derivation and functionality of the determination ofquantization output y(n) from the forced pattern response vectors SPATsand natural input response vector SNAT_(t). As described in Melanson I,the computation reduction scheme 1102 can be expanded or contracted forany look-ahead depth. “C_(Xj)” represents the jth element of naturalinput response vector SNAT_(t) using state variables SV_(N)′, SV_(N-1)′,. . . , SV_(N-J)′, i.e. the filter 1004 output response for the j^(th)element of the M element input vector X_(t) using state variablesSV_(N)′, SV_(N-1)′, . . . , SV_(N-J)′, j={1, 2, . . . , M} and Mrepresents the look-ahead depth. In one embodiment, the filter 1004output response is the summation of state variables SV_(N)′, SV_(N-1)′,. . . , SV_(N-J)′. In general, the filter 904 topology determines thefilter output response. The state variables can be weighted orunweighted. “C_(Yrj)” represents the jth element of the forced patternresponse vector SPAT_(m), r={1, 2, . . . , R} and R=number of forcedpattern response vectors in computation reduction scheme I 102.

As described in Melanson I, in one embodiment quantizer-output selector1104 determines the quantization output y(n) from the output candidatevector associated with (SNAT_(t)×SPAT_(r))_(min). The function generator1100 can also implement functions, using approximated ornon-approximated filter state variables. For example, because of thedominance of later filter state variables, there are instances where thevalue(s) of one or more later state variables are completelydeterminative of the quantization output y(n). For example, if SV_(N) isgreater than A, y(n)=+1, and if SV_(N) is less than −B, y(n)=−1.

Melanson I also describes an add/compare/select (ACS) system 1200depicted in FIG. 12 that can implement function generator 1002 usingapproximated or non-approximated state variables as inputs to determineSNAT_(t). Melanson I recites an example that illustrates the concepts ofACS networks. The operation can be understood as follows. Assume alook-ahead depth of 4 (M=4), and:

-   -   e0=filter response to {1,0,0,0}    -   e1=filter response to {0,1,0,0}    -   e2=filter response to {0,0,1,0}    -   e3=filter response to {0,0,0,1}

Since the filter is a linear system, it follows that SPAT₀=filterresponse to {−1,−1,−1,−1}=−e0−e1−e2−e3. Defining:f 0=e 0·SNATf 1=e 1·SNATf 2=e 2·SNATf 3=e 3·SNATThen:SNAT·SPAT ₀ =−f 0−f 1−f 2−f 3and SNAT·SPAT₁ for any “i” can be computed as a simple sum/difference ofcorresponding f values.

FIG. 13 depicts an exemplary look-up table 1300 of function generator1100. Rows in column 1302 of table 1300 contain the concatenated valuesof approximated state variables used to determine the quantizationoutput y(n). Rows in column 1304 contain the values of quantizationoutput y(n) associated with a corresponding value in column 1302. Theintersection of a row and column is referred to as a record.

The actual values of quantization output y(n) can be determined using avariety of fill-in techniques. Three exemplary fill-in techniques aredescribed below. The value of quantization output y(n) is depicted as anelement of the set {+1,−1}, i.e. a one-bit delta sigma modulator.Multi-bit values can also be determined for y(n) using a multi-bit deltasigma modulator.

Before applying any approximations, state variables are generallyrepresented by at least 10 bits and are typically represented by from 10to 30 bits. The state variables can be approximated by rounding thestate variables to smaller bit sizes, using more rounding for lessinfluential state variables or by other approximation techniques, suchas truncation. As an example, assume that with no approximation statevariables SV_(i) are represented by 10-30 bits. Using approximations,state variable SV_(N)′ is represented by w=6 bits, SV_(N-1)′ isrepresented by v=5 bits, and SV_(N-2)′ is represented by u=4 bits. Theseapproximations require a 32 k (2⁶×2⁵×2⁴) element look-up table 1300.

The table 1300 can be filled in by at least three techniques. In thefirst fill-in technique, because the concatenated state variables areapproximated, each ith value in column 1302 represents a range ofnon-approximated state variable values generally evenly distributed oneither side of the ith value in column 1302. For the ith value in column1302, a quantization output y(n) value can be determined by delta sigmamodulator 900 using the non-approximated state variable located in thecenter of the range of non-approximated state variable values centeredaround the ith value in column 1302. The determined value ofquantization output y(n) is then entered into table 1300 correspondingto the ith value in column 1302. The first fill-in technique isperformed for all values in column 1302. The other state variables(those not used by the table=SV_(N-J-1) through SV₁) are assumed to be 0in this fill-in technique.

In a second fill-in technique, an actual test signal X(n) is used todrive the look-ahead delta sigma modulator 900, using thenon-approximated function generator such as function generator 1100. Theresult statistics are recorded in bins, one bin corresponding to eachtable entry in the approximation generator 1006. The number of y(n)=+1decisions, and the number of y(n)=−1 decisions are recorded. After theend of the test signal, the statistics are evaluated, and for any binthat had a majority of +1's observed, the result is recorded as y(n)=+1in the table 1300. Similarly, for any bin that had a majority of −1'sobserved, the result is recorded as y(n)=−1 in the table 1300. Where notest values are observed (i.e. the test signal did not generate a set ofstate variable values corresponding to an entry in the first column oftable 1300), the first technique can be used to fill in those locations.

In a third fill-in technique, as depicted in FIGS. 14A and 14B, in oneembodiment any time that the state variable SV_(N) of the lastintegrator is (i) greater than A, the quantization output y(n) is alwaysa +1 and (ii) less than −B, the quantization output y(n)=−1, where theabsolute value of A and B may or may not be equal. The values of A and Bare threshold values that are generally dependent upon the delta sigmamodulator implementation and can be empirically determined. Then thefunction can be simplified by making these initial comparisons, makingthe table 1300 smaller. Similarly, further comparisons can be made onother state variables used to determine the quantization output y(n).This technique generally makes for a less accurate function generator,but potentially still much better than the non-look-ahead delta sigmamodulator.

In the instance that a software implementation of function generator1002 is being used, the table look-up process can save many millions ofinstructions per second (MIPs) of computation. The table 1300 can have a3^(rd) state, where either a +1 or a −1 is possible, i.e. thequantization output value is indeterminate from table 1300. In thesecases, the deep search, i.e. standard, full look-ahead calculations areused. In this way, most quantizations can be performed by the table1300, and a small percentage by the standard, full look-aheadcalculation technique. In this way, the average computation load isreduced significantly.

FIGS. 14A, 14B, 14C, 14D, 14E, and 14F depict exemplary embodiments ofnon-linear interrelationships between at least two state variables offilter 904 that, at least in part, characterize one or more boundariesof one or more quantization regions of the quantizer transfer functionQ(s(n)).

FIG. 14A depicts a 2-dimensional slice of an N-dimensional jointlynon-linear function 1400. The Q(s(n)) decision line 1402 represents thenon-linear boundary between two quantization regions, y(n)=+1 andy(n)=−1. The boundary between quantization regions +1 and −1 arecharacterized by the non-linear interrelationship between statevariables SV_(x) and SV_(y) of filter 904. The quantization regions +1and −1 can represent any level of quantization of quantizer 902. Forexample, a one-bit delta sigma modulator has by definition only twolevels of quantization. A multi-bit delta sigma modulator has multiplelevels of quantization. The jointly non-linear function 1400 can definethe quantization regions for any quantization level. Thus, for eachquantization level, the complete jointly non-linear function ismulti-dimensional based on the number of state variables N used todetermine the quantization output y(n).

FIG. 14G depicts a functional implementation to generate Q(s(n)), thejointly non-linear function 1400. In one embodiment, state variableSV_(y) represents a latter (i.e. more significant) state variable, suchas SV_(N), relative to an earlier (i.e. less significant) state variableSV_(x), such as SV_(N)-1. When state variable SV_(y)≧A and statevariable SV_(y)≦−B, the quantizer output y(n) is determined solely bythe value of state of state variable SV_(y). When −B<SV_(y)<A, outputy(n) is determined, for example, by using the lookup table 1300.

FIG. 14B also depicts the non-linear interrelationships between statevariables of filter 904 that characterize boundaries betweenquantization regions of the quantizer transfer function Q(s(n)). Thejointly non-linear function 1404 also depicts multiple quantizationregion boundaries characterized by the non-linear interrelationshipsbetween two state variables, SV_(x) and SV_(y), thus, defining anon-monotonic quantization transfer function for one or morequantization levels. Furthermore, the quantization regions A and D arenonconvex.

FIGS. 14C and 14D depict further embodiments of the non-linearinterrelationships between state variables of filter 904 thatcharacterize boundaries between nonconvex quantization regions of thequantizer transfer function Q(s(n)).

FIGS. 14E and 14F depict further embodiments of the non-linearinterrelationships between state variables of filter 904 thatcharacterize boundaries between non-monotonic, nonconvex quantizationregions of the quantizer transfer function Q(s(n)).

FIG. 15 depicts a PDF 1500 of the quantizer input signal s(n) whenprocessed by quantizer 902. Because of the positive feedback for lowerlevel quantizer input signals x(n), the lower level delta sigmamodulator input signals x(n) are effectively pushed out and the largerlevel delta sigma modulator input signals x(n) more closely conform tothe ideal PDF depicted in FIG. 5B. The delta sigma modulator 900 hasachieved up to 10 db SNR improvement compared to comparable,conventional delta sigma modulators with monotonic quantizers.

Referring to FIG. 16, signal processing system 1600 depicts oneembodiment of a signal processing system that includes delta sigmamodulator 1602. Delta sigma modulator 1602 represents an embodiment ofdelta sigma modulator 900. Signal processing system 1600 is particularlyuseful for high-end audio applications such as super audio compact disk(“SACD”) recording applications. Signal processing system 1600 processesan input signal 1604 generated by an input signal source 1603. The inputsignal 1604 may be digital or analog and may be from any signal sourceincluding signals generated as part of a recording/mixing process orother high end audio sources or from lower-end sources such as a compactdisk player, MP3 player, audio/video system, audio tape player, or othersignal recording and/or playback device.

The input signal 1604 may be an audio signal, a video signal, an audioplus video signal, and/or other signal type. Generally, input signal1604 undergoes some preprocessing 1606 prior to being modulated by deltasigma modulator 1602. For example, pre-processing 1606 can involve aninterpolation filter to oversample a digital input signal 1604 in awell-known manner. Pre-processing 1606 can include an analog-to-digitalconverter to convert an analog input signal 1604 into a digital signal.Pre-processing 1606 can also include mixing, reverberation,equalization, editing, out-of-band noise filtering and other filteringoperations.

In the digital domain, pre-processing 1606 provides discrete inputsignals x[n] to look-ahead modulator 1602. Each discrete input signalx[n] is an N-bit signal, where N is greater than one. As previouslydescribed in more detail, delta sigma modulator 1602 processes M inputsignals x[n] and patterns of M output candidates y[n] to determine anoutput signal 1607 from the output candidates corresponding to eachinput signal x[n]. Output signal 1607 is, for example, a collection ofone-bit output values. The output signal 1607, thus, becomes an encodedversion of the input signal 1604.

Referring to FIGS. 16 and 17, signal processing system 1600 typicallyincludes post-processing 1608 to post-process the output signal 1607 oflook-ahead modulator 1602. Post-processing 1608 can include losslessdata processing 1702. For SACD audio mastering, there is a lossless datacompression stage 1704, followed by a recording process 1706 thatproduces the actual pits that are burned into a master storage medium1708. The master storage medium 1708 is then mechanically replicated tomake the disks (or other storage media) 1712 available for widespreaddistribution. Disks 1712 are, for example, any variety of digitalversatile disk, a compact disk, tape, or super audio compact disk.Playback/output devices 1610 read the data from the disks 1712 andprovide a signal output in a format perceptible to users.Playback/output devices 1610 can be any output devices capable ofutilizing the output signal 1607. Thus, the storage media 1708 and 1712include data encoded using signal modulation processes achieved usingdelta sigma modulator 1602.

Although the present invention has been described in detail, it shouldbe understood that various changes, substitutions and alterations can bemade hereto without departing from the spirit and scope of the inventionas defined by the appended claims.

1. A signal processing system comprising: a look-ahead delta sigmamodulator comprising: a noise shaping filter to process a signal andgenerate N state variables, wherein N is an integer greater than orequal to two; an approximation generator coupled to the noise shapingfilter to generate approximated state variables determined from at leasta subset of the N state variables; and a quantizer coupled to theapproximation generator to quantize quantizer input data determined fromthe approximated state variables and determine a quantization outputvalue with an objective of minimizing quantization error at a currentand at least one future time step.
 2. The signal processing system as inclaim 1 wherein the quantizer comprises a look-up table having recordsof possible approximated state variables and corresponding records ofquantization output values.
 3. The signal processing system as in claim2 wherein each record of possible approximated state variables comprisesa concatenation of approximated state variables.
 4. The signalprocessing system as in claim 2 wherein each ith approximated statevariable record represents a range of non-approximated state variablevalues generally evenly distributed on either side of the ith record andfor each ith record the corresponding quantization output value isdetermined using the non-approximated state variable located in thecenter of the range of non-approximated state variable values centeredaround the ith record.
 5. The signal processing system as in claim 2wherein: each ith approximated state variable record is determined usingan actual test signal X(n) to drive the look-ahead delta sigma modulatorusing non-approximated state variables; the actual test signal comprisesa set of test signal samples associated with the ith approximated statevariable record; the number of quantization output values=+1 decisionsand the number of quantization output values=−1 decisions are recorded;for the set of test signal samples associated with the ith approximatedstate variable record that had a majority of +1's recorded, thequantization output value corresponding to the ith approximated statevariable record is +1; and for the set of test signal samples associatedwith the ith approximated state variable record that had a majority of−1's recorded, the quantization output value corresponding to the ithapproximated state variable record is −1.
 6. The signal processingsystem as in claim 2 wherein any time that a dominant approximated statevariable is (i) greater than A, the quantization output value is a +1and (ii) less than −B, the quantization output value is a −1, wherein Aand B represent predetermined threshold values.
 7. The signal processingsystem as in claim 6 wherein the noise shaping filter comprisesmultiple, cascaded integrators and the dominant approximated statevariable is derived from a state variable of a last integrator of themultiple, cascaded integrators.
 8. The signal processing system as inclaim 2 wherein the records of quantization output values comprisesrecords of indeterminate quantization output values and the quantizerdetermines the quantization output value using non-approximated statevariables of the noise shaping filter each time one of the generatedapproximated state variable corresponds to an indeterminate quantizationoutput value.
 9. The signal processing system as in claim 1 wherein theapproximation generator is configured to generate the approximated statevariables by rounding the subset of the N state variables to smaller bitsizes, using more rounding for less influential state variables.
 10. Thesignal processing system as in claim 1 wherein the look-ahead deltasigma modulator is a one-bit look-ahead delta sigma modulator.
 11. Thesignal processing system as in claim 1 wherein the quantizer comprises alook-up table having records of all possible combinations ofapproximated state variables and corresponding records of quantizationoutput values.
 12. The signal processing system as in claim 1 furthercomprising: a preprocessor coupled between the noise shaping filter andthe approximation generator to preprocess the at least a subset of the Nstate variables.
 13. The signal processing system as in claim 1 whereinthe look-ahead delta sigma modulator comprises a jointly non-linearfunction generator.
 14. The signal processing system as in claim 1wherein the noise shaping filter comprises N integrators and the statevariables represent output values of at least a subset of theintegrators during successive, discrete times.
 15. The signal processingsystem as in claim 14 wherein the subset of the integrators consists ofthe Nth integrator through the N-x^(th) integrators, wherein 2≦x≦N-1.16. The signal processing system as in claim 1 wherein the noise shapingfilter comprises an infinite impulse response filter.
 17. The signalprocessing system as in claim 1 further comprising: a processor; and amemory coupled to the processor and storing processor executable code toimplement the noise shaping filter and the quantizer.
 18. The signalprocessing system as in claim 1 wherein the quantizer input data isderived from audio input signal data.
 19. The signal processing systemas in claim 1 further comprising: signal processing and recordingequipment to process output data from the quantizer and record theprocessed output data on storage media.
 20. A method of processing asignal using a look-ahead delta-sigma modulator that includes a noiseshaping filter having N state variables, wherein N is an integer greaterthan or equal to two, the method comprising: filtering an input signalto the look-ahead delta-sigma modulator using the noise shaping filterto generate the N state variables; generating approximated statevariables determined from at least a subset of the N state variables;and quantizing the quantizer input data determined from the approximatedstate variables to determine a quantization output value with anobjective of minimizing quantization error at a current and at least onefuture time step.
 21. The method as in claim 20 wherein quantizing thequantizer input data determined from the approximated state variablescomprises accessing a look-up table to retrieve a quantization outputvalue record corresponding to a record of the generated approximatedstate variables.
 22. The method as in claim 21 wherein the record of thegenerated approximated state variables comprises a concatenation ofapproximated state variables.
 23. The method as in claim 21 wherein eachith approximated state variable record represents a range ofnon-approximated state variable values generally evenly distributed oneither side of the ith record and for each ith record the correspondingquantization output value is determined using the non-approximated statevariable located in the center of the range of non-approximated statevariable values centered around the ith record.
 24. The method as inclaim 21 further comprising: driving the look-ahead delta sigmamodulator using an actual test signal X(n), wherein the test signal X(n)comprises a set of test signal samples associated with the ithapproximated state variable record; quantizing the test signal X(n)using non-approximated state variables to determine quantization outputvalues for each test signal sample; recording the output values for eachtest signal sample; for the set of test signal samples associated withthe ith approximated state variable record that had a majority of +1'srecorded, recording the quantization output value corresponding to theith approximated state variable record as +1 in the look-up table; andfor the set of test signal samples associated with the ith approximatedstate variable record that had a majority of −1's recorded, recordingthe quantization output value corresponding to the ith approximatedstate variable record as −1 in the look-up table.
 25. The method as inclaim 21 wherein any time that a dominant approximated state variable is(i) greater than A, the method further comprises recording thequantization output value as a +1 and (ii) less than −B, the methodfurther comprises recording the quantization output value as a −1,wherein A and B represent predetermined threshold values.
 26. The methodas in claim 25 wherein the noise shaping filter comprises multiple,cascaded integrators, the method further comprising deriving thedominant approximated state variable from a state variable of a lastintegrator of the multiple, cascaded integrators.
 27. The method as inclaim 21 wherein the records of quantization output values comprisesrecords of indeterminate quantization output values, and the methodfurther comprises determining the quantization output value usingnon-approximated state variables of the noise shaping filter if thegenerated approximated state variable corresponds to an indeterminatequantization output value.
 28. The method as in claim 21 whereingenerating approximated state variables comprises rounding the subset ofthe N state variables to smaller bit sizes, using more rounding for lessinfluential state variables.
 29. The method as in claim 21 whereinquantizing the quantizer input data determined from the approximatedstate variables to determine a quantization output value comprisesquantizing the quantizer input data determined from the approximatedstate variables to determine a one-bit quantization output value. 30.The method as in claim 21 further comprising: preprocessing the subsetof N state variables prior to generating the approximated statevariables.
 31. The method as in claim 20 wherein the input signal datasample comprises audio input signal data.
 32. The method as in claim 20further comprising: recording quantized quantizer input signal data onstorage media.
 33. An apparatus comprising: means for filtering an inputsignal to a look-ahead delta-sigma modulator to generate N statevariables, wherein N is an integer greater than or equal to two; meansfor generating approximated state variables determined from at least asubset of the N state variables; and means for quantizing the quantizerinput data determined from the approximated state variables to determinea quantization output value with an objective of minimizing quantizationerror at a current and at least one future time step.